Mr. Romney’s senior advisers and surrogates flooding the spin room seemed to have one thing above all else on their minds: to deny that Mr. Obama identified the attack in Benghazi, Libya, early on as terrorism, and to scold Candy Crowley, the debate moderator, for backing up Mr. Obama when he said he did just that in the Rose Garden.

“The idea the president called out a terrorist attack in the Rose Garden — Governor Romney’s correct, the president is wrong,’’ said Representative Jason Chaffetz, a Utah Republican who helped lead a House hearing into the attacks last week.

Mr. Chaffetz came armed with a transcript of the president’s spokesman, Jay Carney, stating days later that there was no evidence to back up the claim the attack was preplanned, that it was most likely sparked by an anti-Islamic video.

Tom Ridge, a former Homeland Security secretary under George W. Bush, predicted that the most discussed moment of the debate would be “Candy Crowley’s trying to say on behalf of the president, ‘Well, you did mention terror.’”

“The fact of the matter is,’’ Mr. Ridge said, “the president, his ambassador to the United Nations, his secretary of state and even he himself on multiple occasions talked about that incident as being the consequence of some kind of spontaneous demonstration to that ugly movie.”

In the Rose Garden on Sept. 12, one day after the attack, Mr. Obama said, “No acts of terror will ever shake the resolve of this great nation.”

But others in his administration said for days that the evidence pointed to a spontaneous attack during a demonstration in reaction to the American-made video.

John H. Sununu, the former governor of New Hampshire, flatly asserted, “The president got caught lying tonight, and he’s going to pay a penalty for that.”

Democrats strongly disagreed. David Axelrod, the president’s top stragetist, said Ms. Crowley’s assertion that Mr. Obama “did call it an act of terror” was a highlight of the debate.

“Governor Romney was fact-checked by the moderator when he denied that the president stood in the Rose Garden the day after’’ and referred to the attack as terrorism, Mr. Axelrod said.

Fact-Check: Automatic Weapons

When Mr. Romney was asked about his position on gun control, he erred when he said “We, of course, don’t want to have automatic weapons, and that’s already illegal in this country to have automatic weapons.” Read More

While the sale of new fully automatic machine guns to civilians has been outlawed since 1986, older machine guns were grandfathered into the law and can be sold to civilians in certain states. The law, posted on the Web site of the Bureau of Alcohol, Tobacco and Firearms contains a section called “transfer or possession of machine guns.”

It says: “No person shall transfer or possess a machine gun except: (a) A transfer to or by, or possession by or under the authority of, the United States, or any department or agency thereof, or a State, or a department, agency, or political subdivision thereof. (See Part 479 of this chapter); or (b) Any lawful transfer or lawful possession of a machine gun that was lawfully possessed before May 19, 1986 (See Part 479 of this chapter).”

The National Rifle Association wrote in 1999 that the effect of the law had been “to ‘freeze’ the number of privately owned fully-automatic firearms at roughly 150,000, an exact figure being unavailable due to privacy protection requirements that apply to tax-based laws such as the National Firearms Act.”

Fact-Check: Different From Bush?

When Mr. Romney was asked how he and former President George W. Bush were different, he said they were different people and because the times were different, “my five-point plan is so different than what he would have done.”

But Mr. Romney’s five-point plan, which is light on specifics, is an echo of the platform that Mr. Bush ran on in 2000 – energy independence, education, expanded free trade and a get-tough stance toward China, balanced budgets and small business. As Mr. Romney pointed out, Mr. Bush fell short in those areas, for instance by turning balanced budgets of the Clinton era into annual deficits. Still, their campaign platforms are remarkably similar.

Many conservative commentators quickly trained their sights on a common enemy during the debate: Candy Crowley, the moderator.

Ms. Crowley, they complained, let Mr. Obama speak for longer than Mr. Romney. She fact-checked the Republican without fact-checking the Democrat. And she even told Mr. Romney to take his seat.

One of the lead headlines on the Drudge Report late Tuesday night said, “Candy gives Obama 9 percent more time…”

Laura Ingraham, the author and radio host, said on Twitter, “Candy ALWAYS lets Obama blow the clock…”

But the most serious criticism of Ms. Crowley from the right was focused on her handling of an exchange between the two candidates over Libya and when the president declared the attack on the United States diplomatic mission there a terrorist attack.

Mr. Romney accused the president of waiting 14 days before he declared it an act of terror. Ms. Crowley responded: “He did call it an act of terror.”

Because Mr. Obama was not direct in his remarks — he initially said of the attack “No acts of terror will ever shake the resolve of this great nation” — Republicans have pounced, saying he blamed a video that mocked Islam.

Charles Krauthammer, the columnist and Fox News analyst, accused Ms. Crowley of “contaminating” the debate with her intervention. John H. Sununu, a top Romney adviser, said Ms. Crowley “had no business doing a real-time fact check, if you will, because she was dead wrong.”

But what the conservative pundits have not focused on is that Ms. Crowley also fact-checked Mr. Obama in that same breath, saying, “It did as well take two weeks or so for the whole idea of there being a riot out there about this tape to come out.” She added, addressing Mr. Romney, “You are correct about that.”

Fact-Check: Middle-Class Struggles

Mr. Romney used a series of indicators to argue that the middle class has struggled under the Obama administration. It is true that incomes have fallen and some consumer prices have gone up, even as inflation has increased only mildly.Read More

Mr. Romney said that “the reason I want middle-income taxpayers to have lower taxes is because middle-income taxpayers have been buried over the past four years. You’ve seen, as middle-income people in this country, incomes go down $4,300 a family even as gasoline prices have gone up $2,000. Health insurance premiums — up $2,500. Food prices up, utility prices up.”

It’s true that Americans’ incomes have fallen markedly in recent years, by $4,520 from January 2009 to August 2012, according to Sentier Research’s analysis of Labor Department data.

Overall inflation has been pretty mild, however, thanks to the weak economy. Monthly inflation rates have averaged 0.2 percent over the last four years, about what they were in the previous decade, according to the Labor Department.

That said, there are certain categories of consumer products that have shown bigger price increases that might be more salient for people. Food prices have risen about 7 percent since President Obama took office in January 2009.

Health insurance costs have grown as well. The estimates vary depending on what you are actually measuring and for which population. The average household spent $1,922 on health insurance last year, compared with $1,653 in 2008, an increase of 16.2 percent, according to the Labor Department. The average household spent $3,313 on total health care spending, compared with $2,976 in 2008, an increase of about 10 percent.

On the other hand, household fuel and utility costs, for example, have risen only about 0.6 percent.

Fact-Check: Fast and Furious

Asked for his position on whether to restrict access to assault weapons, Governor Romney brought up Fast and Furious, the botched gun-trafficking case that led to a politically charged oversight investigation by Congress. But Mr. Romney’s description of Fast and Furious, and what is known about it, was misleading in certain significant respects. Read More

Mr. Romney described it as a “program under this administration” under which thousands of weapons “were given to people that ultimately gave them to drug lords” who used them to kill their own people and Americans. He said he could not imagine what its purpose was. He also said that while it had been “investigated to a degree,” it was still unclear “how it worked exactly” or “who it was that did this” and “what the idea was behind it.” He said the Obama administration had asserted executive privilege to “prevent all the information from coming out.”

The operation was exhaustively investigated by the Justice Department’s independent inspector general office, which had access to all the disputed documents and which delivered a 471-page report last month that was praised by members of Congress across party lines as comprehensive and fair.

Operation Fast and Furious was an investigation that ran from late 2009 to early 2011 into a gun-trafficking network in Arizona. The ring was using “straw buyers” – front men without criminal records – to purchase weapons in American gun stores and then funneling them to a drug gang in Mexico, which has much stricter gun-control laws. Contrary to Mr. Romney’s statement, the network was not given guns; rather agents passively allowed suspects to keep buying guns from gun stores rather than moving swiftly to intervene with straw buyers and seize the weapons at the first opportunity.

This tactic – known as “gunwalking” — was internally controversial within the Phoenix Division of the Bureau of Alcohol, Tobacco, Firearms and Explosives because it posed a risk to public safety and ran counter to agency traditions. But its purpose is not a mystery. The agents held back because they were frustrated with bringing cases against low-level straw buyers, who were easily replaced and whose cases presented certain legal challenges in Arizona.They wanted to identify higher-level criminals in the network in order to dismantle the entire organization.

As a result, however, the straw buyers continued to acquire weapons freely, obtaining hundreds of guns that are presumed to have reached criminal hands. In December 2010, two weapons that had been purchased by one of the suspects early in the investigation were found near the site of a shootout where a Border Patrol agent, Brian Terry, was killed, as Mr. Romney alluded.

It is also not a mystery who was behind it, and it is somewhat misleading to limit the discussion to the particular operation that took place during the Obama administration. The inspector report concluded that poorly supervised Arizona-based law enforcement officials had developed the gunwalking tactics on their own. It also found that they had used a similar strategy and tactics in an investigation of another Arizona-based gun smuggling network starting in 2006, a case called Operation Wide Receiver. In particular, the report said that William Newell, the special agent in charge of the A.T.F.’s field division in Phoenix at the time of Fast and Furious and part of Wide Receiver, “bore ultimate responsibility for the failures in Operation Fast and Furious.” The report also found that the field division had not alerted A.T.F. headquarters about its use of the tactics, and that no one at Justice Department headquarters, under either the Bush or the Obama administrations, had authorized or knew about each operation’s tactics at the time they were being used.

Mr. Romney is correct that President Obama asserted executive privilege to shield some Justice Department documents from a Congressional subpoena. The disputed documents do not date from the origins of Fast and Furious, however. They are from after February 2011, by which time the operation was over. The documents – many of which the inspector general quoted from in its report – are e-mails in which officials discussed how to respond to Congressional inquiries and media questions as they struggled to figure out what happened. Mr. Obama has claimed he has a legal right not to comply with the subpoena for them because it would damage the candor of internal executive branch deliberations to allow Congress to compel their disclosure. That dispute is now the subject of a lawsuit filed by Congress.

Fact-Check: Romney Said Tax Rate Was 'Fair'?

Mr. Obama accused Mr. Romney of saying in a ”60 Minutes” interview that he believed it was “fair” that he paid a lower tax rate than ordinary workers like bus drivers. Mr. Obama simplified the question Mr. Romney was asked by CBS’s Scott Pelley and Mr. Romney’s response.Read More

This was the full exchange, which focused on the fairness of the capital gains tax rate:

PELLEY: Now, you made on your investments, personally, about $20 million last year. And you paid 14 percent in federal taxes. That’s the capital gains rate. Is that fair to the guy who makes $50,000 and paid a higher rate than you did?

ROMNEY: It is a low rate. And one of the reasons why the capital gains tax rate is lower is because capital has already been taxed once at the corporate level, as high as 35 percent.

PELLEY: So you think it is fair?

ROMNEY: Yeah, I — I think it’s — it’s the right way to encourage economic growth, to get people to invest, to start businesses, to put people to work.

Doug Mills/The New York TimesMitt Romney and President Obama pointed fingers at each other during the second presidential debate at Hofstra University in Hempstead, N.Y.

“This time, President Obama showed up.”

That was the conclusion of the Democratic analyst Joe Trippi on Fox News immediately after Tuesday’s debate, echoed by commentators on the Internet and on all the major networks.

Brit Hume, seated next to Mr. Trippi on Fox, said Mr. Obama would “probably be declared the winner on most cards.”

Indeed, on ABC, the conservative columnist George Will said, “Barack Obama not only gained ground that he had lost, he cauterized some wounds that he inflicted on himself by seeming too distant and disengaged.”

On CNN, the longtime analyst David Gergen said “the night goes to Barack Obama.” On MSNBC, the Rev. Al Sharpton credited Mr. Obama with his “best performance of his career as a debater.”

“Tonight Mitt Romney was up against a different man,” said the MSNBC host Rachel Maddow, who added that “Democrats will be thrilled.”

Republicans tended to call the debate a draw, as the former George W. Bush press secretary Ari Fleischer did on Twitter at the halfway mark and again after the debate.

As the second hour of the debate began, another former Bush press secretary, Dana Perino, wrote on Twitter, “As everyone predicted, each side will be able to say their candidate did well tonight.” She predicted that the mainstream media would say, “Obama stops slide.”

Most of the focus afterward was in fact on Mr. Obama, although Ben Smith of Buzzfeed noted, “Romney did, again, come away looking like a guy who could be president, which is probably the most important thing.” Steve Schmidt, the Republican strategist, said on MSNBC, “I’m not sure that the president’s performance is enough to arrest Mitt Romney’s momentum in the race.”

Either way, there was this observation from Mr. Will on ABC, a compliment to both candidates and to the moderator, Ms. Crowley: “I have seen every presidential debate in American history, since the four of Nixon and Kennedy in 1960. This was immeasurably the best.”

And so he did. The day after the attack in Libya, Mr. Obama, in the Rose Garden, said: “No acts of terror will ever shake the resolve of this great nation, alter that character, or eclipse the light of the values that we stand for.”

He didn’t say it again in the weeks after, which is why Mr. Romney made his accusation. But it is incorrect to say that Mr. Obama did not initially call the attack an “act of terror.”

Brian Blanco for The New York TimesScott Nystrom watched the second presidential debate in Largo, Fla.

LARGO, Fla. – If undecided voters are often also “low information voters,” then the independents here Tuesday night would certainly fall into the category of high information voters. Three are retirees who spend a lot of their time reading news. And Mr. Nystrom, the waiter, is a close follower of economic data across the states because he is hoping to leave Florida for a better job. He has a college degree in technology, and he has not been able to use it around Largo.

As such, these viewers have as many answers as the candidates, and they suggested that the answers the candidates provided actually open a host of new questions that, for now, will go unanswered. They did not watch this debate passively. They were active participants.

On the issue of trade with China, for instance, Mr. Bach, Ms. Siegrist, Mr. Nystrom and Mr. Fechko had so much to say, they drowned out the television for a moment.

“China is never…

“Romney doesn’t….

“Guys, guys!”

“Quiet.”

Then came the concluding statements.

“The last question was the best part of the debate for the president,” Mr. Bach said. “He came out strong. He turned the debate of two weeks ago totally around. There was no comparison. He brought out his passion and his experience and his concern. Romney played defense a lot of the night.”

Romney was faulted for reversing himself too much.

“I’ve watched 20 of the 22 Republican debates and I don’t like that Romney has positions now that he did not have previously,” Mr. Fechko said, listing issues such as abortion, immigration and taxes.

But Mr. Obama was also faulted for his “wishy-washy” position on gun control and because his statement on the attack in Libya seemed weak.

The group did not like the terms winner and loser, but the consensus seems to be this:

“If people are using the debates only as their guide as to how they will vote, then Obama certainly helped himself tonight,” Mr. Fechko said.

Fact-Check: U.S. Military Spending at 4% of G.D.P.

In a rapid-fire exchange on dueling tax rate plans, Mr. Obama said Mr. Romney wanted to give tax breaks to the wealthy – which he said would decreases government revenue, but then add large sums to the military budget, as well. Like all statistics, these on military spending can be viewed from different angles to offer different perspectives.Read More

“Governor Romney then also wants to spend $2 trillion on additional military programs, even though the military’s not asking for them,” Mr. Obama said.

In the previous debate, of the vice presidential candidates, Mr. Romney’s running mate, Paul D. Ryan, denied that the Republicans proposed to increase military spending more than $2 trillion over a decade. But the Pentagon would need $2.3 trillion more than is projected through fiscal year 2022 at current spending levels, adjusted for inflation.

That is because military spending as a share of the economy’s total output is expected to dip below 4 percent of the gross domestic product later in the decade. To keep it at that level would require the additional spending. The drop in military budgets as a share of G.D.P. is due less to any reductions for the Pentagon and more to the fact that a growing piece of the federal budget pie is being consumed by spending for entitlement programs like Medicare, Medicaid and Social Security as more baby boomers reach retirement age.

To be sure, Mr. Romney has vowed to spend at least 4 percent of the nation’s gross domestic product on national defense. In setting that goal, he has lots of company: Mr. Obama’s first chairman of the Joint Chiefs of Staff, Adm. Mike Mullen, also urged early in his tenure that military spending never drop below 4 percent of the gross domestic product.

Yet both Admiral Mullen and the defense secretary with whom he worked the most, Robert M. Gates, also came to realize that the nationwide economic downturn meant that the fire hose of money flowing to the Pentagon after the attacks of Sept. 11, 2001, was no longer sustainable. Both Admiral Mullen and Mr. Gates then pushed ahead with a sweeping series of defense spending adjustments, including canceling or slowing some weapons programs, shrinking the size of the military’s personnel rosters and slimming the civilian bureaucracy. Those cuts have been taken ever deeper under Mr. Obama’s current defense secretary, Leon E. Panetta.

Regardless of who is the next president, he will have to shape his military budgets based on two realities: the nation’s economic condition – and a Congress that carries out its own agenda on defense.

The wars of today are fought differently, with different weapons that offer more bang for the buck than earlier generations. And today’s national security environment requires a different size force.

Since the collapse of Communism in Eastern Europe, the military’s roster has shrunk. Remember those (expensive) heavy armored divisions standing watch across the Fulda Gap in Germany to deter the Soviet Army? Gone. The arsenal of bombers, attack jets, warships and nuclear warheads has diminished, as well, as the White House and Pentagon tried to fit defense dollars to the changing national security environment.

And the public’s representatives in Congress, where the budgets must be approved, have made clear that there is no appetite for paying the tab for a large standing military sized to the needs of 1970. After all, personnel costs are the largest part of the Pentagon budget.

Defense Department spending doubled in the decade since the terrorist attacks of Sept. 11, 2001, but deficit-reduction measures urged by both Democrats and Republicans have forced the Defense Department to reduce budget proposals for the next decade.

To hit those deficit-reduction targets, the Obama administration has offered more than $450 billion in cuts that would reduce the military budget by roughly 7 percent or 8 percent over the next 10 years, even beyond the spending reductions that are expected to come naturally from the withdrawals first from Iraq and from Afghanistan.

The Obama White House and the Pentagon are joined at the hip in urging Congress to reach a budget deal that would avert even deeper cuts in military spending in a process of across-the-board reductions call sequestration.

Fact-Check: Broken Promise on Immigration Reform?

“Now, when the president ran for office,” Mitt Romney said, “he said that he’d put in place, in his first year, a piece of legislation — he’d file a bill in his first year that would reform our — our immigration system, protect legal immigration, stop illegal immigration. He didn’t do it.” Mr. Romney is right about that, and some Latino voters have been disappointed.Read More

President Obama made the promise, particularly to Latinos, during the summer of 2008. In an interview with Jorge Ramos of Univision, the Spanish-language network, he said, “What I can guarantee is that we will have in the first year, an immigration bill that I strongly support.”

When he has come under attack from Mr. Romney during the campaign for failing on that promise, Mr. Obama has largely blamed Republicans. At a new encounter with Mr. Ramos at a town hall meeting in Miami last month, Mr. Obama said he had not anticipated that Republicans who previously supported reform “suddenly would walk away.”

One measure of Mr. Obama’s efforts was the attempt in December 2010 to pass the Dream Act, a bill that would give legal status to at least 1.2 million young undocumented immigrants who came to the United States when they were children. After an intense campaign by the White House, the bill passed the House of Representatives. In the Senate, it failed — by five votes — to gain the 60 votes needed to go to the floor. Five Democrats voted against the bill. But all Republicans but three voted against it, including many who had supported it in the past, giving the president grounds to say the Dream Act was “blocked by Republicans.”

Last month in Miami, Mr. Obama said his lack of progress on immigration legislation was “my biggest failure so far.” With no prospect of passing legislation in Congress, Mr. Obama used executive authority in June to offer reprieves from deportation to hundreds of thousands of young undocumented immigrants.

Fact-Check: Employing Women in Massachusetts

Mr. Romney said that as governor, he employed more women in senior state government positions than did any other state administration, but there have been conflicting reports as to whether that is the case.Read More

A 2004 study by the University of Albany Center for Women in Government and Civil Society supported that contention; according to that study, 50 percent of Massachusetts policy-making posts were held by women in 2003, compared with an average of 32 percent for state governments as a whole. But Factcheck.org, of the Annenberg Center on Public Policy, took a different position: over Mr. Romney’s four years as governor, it stated, 31 percent of all appointments were women. And the share of women named to senior-level posts actually declined slightly, to 27.6 percent, it said. The organization said that a Romney administration work force official “cherry-picked statistics to make Romney’s record on appointing women to government positions look better than it is.”

Fact-Check: Fewer Women Have Jobs?

Governor Romney criticized President Obama’s economic performance by saying that fewer women have jobs than four years ago. But that is not correct, according to the Bureau of Labor Statistics.Read More

Mr. Romney said: “In the last four years, women have lost 580,000 jobs. That’s the net of what’s happened in the last four years.” But according to the Bureau of Labor Statistics, there are 253,000 more women working in the United States than was the case in January 2009, when President Obama took office. According to the B.L.S., there were 67,222,000 women working this September, while the bureau said there were 66,969,000 women working in January 2009.

Fact-Check: Calling China a Currency Manipulator

Mr. Romney said that China had been artificially holding down the value of its currency for years and that President Obama had passed up the opportunity to label China as a currency manipulator. Though the Obama administration has never named China as a currency manipulator, no other administration since 1994 has.Read More

Every six months, the Treasury Department issues a report in which it can identify nations as currency manipulators. The Obama administration has never named China as a currency manipulator. Nor has any administration since 1994, opting instead for behind-the-scenes pressure that has prodded China to let its currency, the renminbi, rise.

Since 2005, the renminbi has appreciated about 30 percent against the dollar, according to a July report by the International Monetary Fund that revised the renminbi’s status from “substantially” to “moderately undervalued.” Mr. Romney’s advisers have said that China has more recently intervened to weaken the currency. But Michael Pettis, a finance professor at Peking University and a senior associate at the Carnegie Endowment, says that while the renminbi has fallen by 1 percent since February, the fall is a result of capital flight, not government intervention.

Even if the United States formally identified China as a currency manipulator, that in itself would only trigger bilateral consultations. Economists point out that the United States and China are already negotiating over the renminbi’s value — and have been for many years. Mr. Romney has promised that if China does not compromise, he will follow up by instructing the Commerce Department to impose countervailing duties on Chinese imports on a case-by-case basis. Economists warn that that might trigger a trade war with China in which both sides lose.

Toward the end of the debate, Mr. Romney and Mr. Obama had a spirited back and forth on exports and manufacturing jobs. Mr. Obama has campaigned on his record of bringing back manufacturing jobs to America, but Mr. Romney has argued that manufacturing jobs have shrunk on Mr. Obama’s watch.

Both candidates have a point.Read More

Manufacturers have about 610,000 fewer employees on payroll than they did when Mr. Obama took office. But Mr. Obama took over when the economy was still in free fall, months before the worst recession since the Great Depression ended and months more before employers felt confident in adding workers. Manufacturing firms started adding jobs in mid-2010, and have added about 400,000 positions since then.

Mr. Obama has furthermore promised to create one million new manufacturing jobs in the next four years. How realistic is the goal? It could certainly happen. Manufacturing employers would need to add about 21,000 workers per month for the next four years. In the past year, they have added about 14,500 new workers a month.

Even if the economy added those million manufacturing jobs, though, it would not imply that manufacturing has really recovered as a jobs powerhouse, or ever will. By the end of 2016, Mr. Obama wants there to be about 13 million manufacturing jobs in America. That is about the same number of manufacturing jobs there were when he won election in 2008.

And here they come! Even before the debate had ended, the spinners had flooded the zone of the press filing center. The Democrats arrived first, with blue signs proclaiming Axelrod, Schumer, Psaki and Kerry. They were quickly swarmed by the gentlemen and ladies of the press. A few minutes later came an influx of red signs with Republicans: Sununu, Jindal and Chaffetz. First the two teams were on opposite sides of the room, but now blue and red are intermingling.

Fact-Check: Romney on the Dream Act

“Now, Governor Romney just said that, you know, he wants to help those young people, too,” President Obama said, referring to young undocumented immigrants. “But during the Republican primary, he said, I will veto the Dream Act that would allow these young people to have a chance.” Since the primaries, Mitt Romney has softened his position on the Dream Act, a bill that would give legal status to young undocumented immigrants who came to the United States as children. But not by much.Read More

Mr. Romney did say during the primaries that he would veto the Dream Act, a measure supported mainly by Democrats that has long been stalled in Congress. In June, Mr. Romney shifted his position to say he would support giving legal resident green cards to “illegal immigrants who served in our military” — one group who would be eligible under the Dream Act.

In a town hall meeting last month in Miami with Univision, the Spanish-language network, Mr. Romney said he would also consider giving green cards to “kids that get higher education,” echoing another part of the Dream Act. But Mr. Romney said he preferred the approach of Senator Marco Rubio, a Republican from Florida who started work last spring on an alternative to the Democrats’ bill.

However, few details are known of Mr. Rubio’s proposal, because he never offered a written blueprint. In June, after President Obama announced he would give temporary reprieves from deportation to young immigrants — in part to upstage Mr. Rubio — the senator set aside his efforts.

Under the Dream Act, by independent estimates at least 1.2 million young undocumented immigrants could be eligible for legal status.

Fact-Check: Daylight on Israel?

Mr. Romney said that “the president said that he was going to put daylight between us and Israel.” Is he correct?Read More

Mr. Romney’s campaign cites a newspaper account of a meeting with Jewish leaders at the White House in 2009 as evidence for Mr. Romney’s statement. In that account, published in The Washington Post, people at the meeting said Mr. Obama had said that “there was no space between us and Israel” during the George W. Bush administration, which he said had hurt the ability of the United States to influence Israeli actions or cajole Arab nations. “When there is no daylight, Israel just sits on the sidelines, and that erodes our credibility with the Arab states,” the newspaper quoted Mr. Obama as saying.

An Obama administration official said they did not know whether Mr. Obama made that statement during what was a private meeting.

The newspaper account did not quote Mr. Obama as explicitly stating that his goal was to put distance between the United States and Israel, as Mr. Romney characterized Mr. Obama’s intentions during a recent speech. Instead, the account indicates Mr. Obama was complaining that what he suggested was the Bush administration’s unwillingness to challenge the Israelis had reduced the American government’s leverage over Israel and hurt its reputation with Muslim countries. At the same time, a plain reading of the account would also suggest that Mr. Obama wanted for his administration to be seen as less of a rubber stamp for Israel than the Bush administration was.

Obama administration officials have said that there is no daylight whatsoever between the United States and Israel on the issue of preventing Iran from obtaining nuclear weapons.

A broader question is how much “daylight” there has been between the two countries since Mr. Obama took office. Mr. Obama angered some Israeli leaders, like Benjamin Netanyahu, the prime minister, by publicly stating that Israel’s 1967 borders adjusted though land swaps should be the starting point for settlement negotiations with the Palestinians, and by pushing Israel to curb settlement construction in the West Bank.

But many experts are puzzled by the Romney camp’s claim that Mr. Obama has been weak on Israel, saying the opposite is actually true. Even Israel’s own defense minister – and former prime minister – Ehud Barak has repeatedly and enthusiastically praised Mr. Obama’s support, telling CNN in July: “I should tell you honestly that this administration under President Obama is doing in regard to our security more than anything that I can remember in the past.” Other experts cite Mr. Obama’s extensive military aid to Israel, as well as his unwavering opposition at the United Nations to Palestinian statehood.

Fact-Check: Romney on Immigration

What is Mr. Romney’s strategy on illegal immigration? His positions have varied over the past year, but he says he opposes amnesty for illegal immigrants in most cases.Read More

President Obama said that Mitt Romney’s “main strategy” to curb illegal immigration would be to “encourage self-deportation.”

Mr. Romney has never precisely clarified what he would do about more than 11 million illegal immigrants in the United States. During the Republican primaries he called for tough enforcement to pressure them to leave the country. Since June he has moderated that position, saying he could support some measures that would allow a limited group of illegal immigrants to remain here legally.

Mr. Romney says he opposes any amnesty. During a primary debate in January, he said he would seek a mandatory nationwide program to verify the legal status of all new hires, expanding an existing federal program known as E-Verify, which currently is voluntary. With that program in place, he said, illegal immigrants would soon discover they could not get jobs and “they’re going to self-deport.”

Mr. Romney was pressed for more details on the self-deportation strategy during a town hall meeting last month in Miami with Univision, the Spanish language network. But he did not provide them. “I believe people make their own choices as to whether they want to go home,” he said.

But he said he would not favor “a mass deportation effort, rounding people up, 12 million people.” Mr. Romney said, “Our system is not to deport people.”

He has said he would support giving permanent resident green cards to illegal immigrants who serve in the military — probably a group numbering tens of thousands. Mr. Romney has said he would “put in place a permanent solution” for illegal immigration, but he has not described what it would look like or how he would get around the roadblocks in Congress that stalled President Obama’s efforts to pass legislation. Most Republican lawmakers in Washington have rejected any legal status for illegal immigrants, calling it amnesty.

Fact-Check: 'Pioneers of Outsourcing?'

Mr. Obama accused Mr. Romney of investing in companies that were pioneers in outsourcing to China. Is this true?Read More

This is a tweak of a long-running attack line the Obama campaign has used against Mr. Romney, based on investments made by the private equity firm he founded, Bain Capital. This time Mr. Obama softened the blow by accusing Mr. Romney of merely investing in the companies, as opposed to being more directly involved in those outsourcing decisions.

Fact-checkers, including Politifact.com, FactCheck.org and the Washington Post’s Fact Checker column, had questioned the more direct line of attack on outsourcing, because most of the companies cited by the Obama campaign were investments that occurred after Mr. Romney had left day-to-day management of Bain in 1999 to run the Winter Olympics in Salt Lake City. Mr. Romney was indisputably involved with at least one Bain-owned company that outsourced jobs overseas — to China, in particular — Holson Burnes Group, a picture frame and photo album manufacturer that Bain owned from 1987 to 1995.

But FactCheck.org, which examined the issue, pointed out that it was unclear whether the company’s outsourcing increased or decreased under Bain, or if the manufacturing overseas came at the expense of American jobs.

The question of whether Bain Capital ever invested in such companies, with Mr. Romney benefiting as an investor, is a much less controversial one. Several of Bain’s investments did have operations in China, although it would be a stretch to call them “pioneers” in the practice.

It is also important to point out that since 2002, when he was elected governor of Massachusetts, Mr. Romney’s investments have been managed through an independent trustee.

One question heading into the debate: how would the president handle Secretary of State Hillary Clinton’s acceptance of responsibility for the violence in Libya?

His decision was to embrace the responsibility.

“Secretary Clinton has done an extraordinary job,” he said. “But she works for me.”

He also was aggressive in pushing back against Mr. Romney’s accusation that his administration has played politics in the aftermath of the killings of four Americans in Libya.

Looking straight at Mr. Romney, he said: “The suggestion that anybody on my team, the secretary of state, our U.N. ambassador, anybody on my team, would play politics or mislead, when we’ve lost four of our own, is offensive, Governor.”

LARGO, Fla. – On the issue of the recent attack on American diplomats in Benghazi, Libya, Mr. Romney is criticizing the president.

“I’m waiting for him to say it was the president’s fault, which it seems he is hinting at,” Mr. Bach said.

Mr. Romney was critical of Mr. Obama for taking many days to acknowledge that the attack was terrorism.

But when Ms. Crowley supported the president’s assertion that he called the attack an act of terror in the Rose Garden on the day after it happened, Mr. Bach said, “That’s right, no distortions tonight, my friend!”

It seems clear by now that Mr. Bach is leaning toward favoring the president. But he is not completely on board.

When the question turned to gun control and Mr. Obama began a long anecdote, Mr. Bach spoke loudly toward the television: “O.K., O.K. What’s your policy, sir? Answer!”

“He broached it but didn’t answer it completely,” Mr. Bach said.

Mr. Nystrom added: “It’s such a tough issue. It’s like a lost cause.”

Mr. Fechko said: “You could see Obama sort of dancing around it, because he knows he can’t come flat out for gun control in the current environment.”

Fact-Check: Terrorism and Security in Libya

The Obama administration has drawn criticism for shifting assessments of what really happened in Benghazi, Libya, and for questions of security at the diplomatic mission there.Read More

Asked who had denied added security that was requested for embassies in Libya, Mr. Obama did not directly answer, although he did say, “I am ultimately responsible for what’s taking place there.” Mr. Romney questioned why “it took a long time” for the facts to come out.

The Obama administration has come under fire for shifting assessments of what really happened in Benghazi – and what happened before Benghazi.

The administration initially described the attack on the diplomatic post as a spontaneous outgrowth of protests against an anti-Islam video made in the United States. Days later, officials termed it a terrorist attack planned by Islamic extremists and dropped references to any protest.

Journalistic reporting from Libya indicates that the video was a motivating factor for many who participated in the attack but there was no protest; the assailants have been described as members of Ansar al-Shariah-Benghazi, a local Islamist extremist group that shares ideological commonalities with al Qaeda but not its international aspirations and has not been shown to have direct organizational ties.

Americans on the ground sounded increasing alarms about the dicey security situation in the months leading up to the attack, and two security officials testified before Congress last week that they sought to keep more security personnel for Libya but were turned down by the State Department in Washington.

The requests were for more guards in Tripoli, rather than in Benghazi, and State Department officials testified that they would not have stopped the attack even if the requests had been approved. Vice President Joseph R. Biden Jr. said at last week’s debate that the White House was not made aware of those requests.

The Obama team has hit back at Republican critics by claiming that House Republicans cut $300 million from embassy security. Congress did make relatively small cuts after Republicans took control in the 2010 elections. For the current fiscal year, House Republicans voted to increase spending on diplomatic security by about $250 million, still about $220 million less than Mr. Obama requested. A State Department official testified that security decisions in Libya were not affected by budget constraints.

Fact-Check: Romney and Arizona Immigration Law

Mitt Romney’s statements about immigration measures in Arizona have been widely misquoted by Democrats — and were misquoted again Tuesday night by President Obama — to make it appear he embraced as his “model” a tough and polarizing police enforcement law in that state.

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It is true that Mr. Romney has spoken favorably of Arizona’s police law, known as S.B. 1070. He defended the state’s decision to pass it and he criticized President Obama for bringing a lawsuit to try to stop it. But what Mr. Romney calls his model is a less controversial law that made it mandatory for Arizona employers to use a federal electronic verification system, known as E-Verify, to check the immigration status of new hires.

“What I like about the Arizona law was a measure that says we’re going to have an employment verification system so that employers know who they’re able to hire and who they’re not able to hire,” Mr. Romney said last month, speaking to a Latino audience in a televised town hall meeting in Miami.

President Obama is right that Mr. Romney embraced some immigration hard-liners early in the campaign. During the primaries Mr. Romney welcomed the endorsement of Kris Kobach, a conservative lawyer who is now secretary of state of Kansas, and who was an author of Arizona’s police law. He has also provided templates for tough immigration enforcement bills in many other states. Mr. Kobach’s law-and-order views are regarded as extreme by many Latino and immigrant rights groups. More recently Mr. Romney has played down the role of Mr. Kobach in his campaign.

By the way, President Obama also supports mandatory worker verification, but only as part of a package that includes legal status and work authorization for millions of illegal immigrants.

Fact-Check: Contraceptive Coverage

Mr. Obama mentioned a provision of his signature health care law that requires most insurance plans offered by employers to provide free birth control. Mr. Romney, he said, opposes the requirement and believes that “employers should be able to make the decision” as to whether their female workers get contraceptive coverage.

Mr. Obama was correct: Mr. Romney is against the requirement, which he has described as an attack on religious liberty Mr. Romney has said he would abolish the requirement.Read More

Churches were exempt from the requirement when the Obama administration announced it last year. Still, it provoked furious criticism from Roman Catholic institutions and other religious and conservative groups, who called the exemption too narrow.

In February, the administration offered what Mr. Obama described as ”an accommodation” for church-affiliated schools, universities, hospitals and charities that object to the requirement. Under that plan, which has yet to be finalized, such institutions would not have to “pay for, provide or facilitate the provision of” contraceptive coverage. But their female employees could get such coverage directly from their insurance companies at no cost.

Roman Catholic bishops and other conservatives were not appeased by the compromise proposal. One of their concerns is that some religiously affiliated organizations choose to insure themselves. They also say it is impossible to guarantee that the premiums paid by objecting organizations for their employees’ overall medical coverage would not help finance birth control.

Mr. Romney supported a Republican effort, known as the Blunt amendment, that would have let any employer or insurance company deny coverage for contraceptives and other items they objected to on religious or moral grounds. But the Senate in March narrowly voted to kill the effort.

Opponents have filed at least 35 lawsuits around the country seeking to have the contraception requirement overturned.

Fact-Check: Tariff on Chinese Tires

President Obama said, “We had to make sure that China was not flooding our market with cheap tires” and therefore took action to save 1,000 jobs. It is true that in 2009, the Obama administration imposed a duty on Chinese tires, but last month the administration let the tariff expire.Read More

The United Steelworkers Union, an Obama political supporter, sought the action, and many economists criticized it as politically motivated.

A study by the Peterson Institute for International Economics found that the tariff protected at most 1,200 American jobs. But last year alone. the institute found, it cost American consumers $1.1 billion in higher-priced tires.

Moreover, China responded by imposing tariffs on imports of American chicken parts that cost American poultry producers an estimated $1 billion. Last month, the Obama administration quietly let the tire tariff expire. Critics say that it recognized the economic costs of the sanction were too great.

Brian Blanco for The New York TimesErnie Bach reacted as he gathered with friends to watch the second presidential debate in Largo, Fla.

LARGO, Fla. – Will the next four years be like the last four years? And has Mr. Obama kept his promises? An unenthusiastic audience member who voted for Mr. Obama in 2008 wanted to know.

Mr. Romney argued that Mr. Obama’s policies had crushed the middle class, but Mr. Obama stated a list of his accomplishments, what he called promises kept, including killing Osama bin Laden and passing health care reform.

“The question, are you better off?’’ Mr. Bach said. “Nobody’s asking, ’Are you worse off than four years ago?’ That’s what I want to know.”

Ms. Siegrist, who is taking notes on a legal pad with a pencil, interjected: “Well, there are an awful lot of poor people. The numbers keep multiplying.”

The topic turned to immigration.

Now Mr. Bach is furiously scribbling on his notepad as Mr. Obama describes the Dream Act.

“We have a prime example in Florida of what Obama is talking about, a high school valedictorian who finished at the top of his law class and can’t get a license because he’s illegal,” Mr. Bach said.

After a tense exchange between the candidates about overseas investments that diverted significantly from the topic of immigration, Mr. Nystrom asked: “Did the moderator just ask them to sit down? What’s going on?”

Fact-Check: Doubling the Deficit?

Mr. Romney just repeated the false charge — which he also made during the first debate — that Mr. Obama has doubled the deficit.

“He said when he was running for office, he would cut the deficit in half,” Mr. Romney said of Mr. Obama on Tuesday night. “Instead he’s doubled it.”

The Congressional Budget Office just announced that the federal budget deficit was about $1.1 trillion in 2012, approximately $200 billion less than the shortfall recorded in 2011. Measured as a share of the economy, as economists prefer, the deficit has declined more significantly — to 7.0 percent of the economy’s total output in 2012 from 10.1 percent in 2009.

Fact-Check: Obama Unemployment Promises?

Mr. Romney charged that Mr. Obama promised the unemployment rate would be 5.4 percent by now. (It is currently 7.8 percent.) This is an old canard based on a report released before Mr. Obama even took the oath of office. Read More

Two economists with the incoming administration, Jared Bernstein and Christina Romer, ran some numbers estimating the job creation potential of a stimulus bill to arrest the economy’s free fall. They forecast that if such a bill were enacted, unemployment would never rise above 8 percent and would fall to about 5.4 percent by now.

But that was a projection made before economists really understood the severity of the recession, the historic plunge in output and huge job losses. Moreover, it was a projection by White House economists, not a promise Mr. Obama made.

Fact-Check: Changes in Romney Tax Policy?

Has Mr. Romney’s position on tax cuts for the wealthy changed? While he said here that “I’m not looking to cut taxes for wealthy people,” this is a shift from his statements during the Republican primary race.Read More

Mr. Romney said Tuesday night that “I’m not looking to cut taxes for wealthy people” — which, as Mr. Obama noted, is a change from how he described his tax plans during the Republican primaries.

At a Republican primary debate this winter, when Rick Santorum charged that Mr. Romney might raise taxes on “the top 1 percent,” Mr. Romney countered, “We’re going to cut taxes on everyone across the country by 20 percent, including the top 1 percent.”

Mr. Obama noted the change Tuesday night. “And when Governor Romney stands here, after a year of campaigning, when during a Republican primary he stood on stage and said, ‘I’m going to give tax cuts’ — he didn’t say tax rate cuts, he said ‘tax cuts to everybody,’ including the top 1 percent, you should believe him because that’s been his history,” Mr. Obama said.

Damon Winter/The New York TimesMitt Romney and President Obama at the debate in Hofstra University in Hempstead, N.Y.

Mr. Romney just landed on what is the strongest argument any challenger running against an incumbent, particularly an incumbent in charge during difficult times. He ran through a list of statistics showing the extent to which the economy has struggled under Mr. Obama and offered a compliment that would have sounded discordant at the last debate: That Mr. Obama is a great speaker.

Fact-Check: Romney Investment in Chinese Company

President Obama said Mr. Romney invested in a Chinese company that conducted video surveillance on citizens. Is that correct?Read More

The investment was actually made through a fund managed by Bain Capital, the private equity firm Mr. Romney founded and ran until 2001. Mr. Romney has as much as $2.25 million invested in three Bain Capital funds with sizable stakes in at least seven Chinese companies,including an electronics retailer accused of selling computers with pirated Microsoft software. He has millions more invested in Bain funds that control an auto parts company that is closing a United States factory and moving equipment and jobs to China.

Mr. Romney says his fortune is managed by a blind trust over which he has no control. However, the trust, managed by a law firm that also works for Bain Capital, would most likely not meet federal requirements for independent management should he become president because of the close relationship between the law firm, Mr. Romney and Bain.

Doug Mills/The New York TimesMitt Romney and President Obama interacted with Ms. Crowley, the moderator, during the debate at Hofstra University in Hempstead, N.Y.

Mr. Obama aggressively raised the issue of contraception — an issue that he all but ignored at the first debate with Mr. Romney.

Focusing on the impact of Mr. Romney’s policies on women — and with an eye, no doubt, on the all-important women’s vote — Mr. Obama accused him of doing harm to women and families.

“A major difference in this campaign is that Governor Romney feels comfortable having politicians in Washington decide the health care decisions” for women, Mr. Obama said.

He accused Mr. Romney of wanting to eliminate financing for Planned Parenthood and of opposing the policies that make contraceptives affordable.

“These are not just women’s issues; these are family issues. These are economic issues,” Mr. Obama said. “I’ve got two daughters, and I want to make sure that they have the same opportunities that anyone’s sons have.”

When he got the chance, Mr. Romney accused the president of distorting his proposals.

“I just note that I don’t believe bureaucrats in Washington” should control health care decisions for women, he said. “Every woman in America should have access to contraceptives.”

Twitter, the social network of choice among political reporters, pundits and those who love them, is also the new spin room — and it saw a tremendous reaction to President Obama and Mitt Romney’s first few answers to voter questions about jobs and energy.

The first questioner, a college student named Jeremy, was quickly christened the new “Joe the Plumber” — a reference to the Ohio man who asked Mr. Obama about taxes during a campaign stop in 2008 and became a metaphor for the middle class. The candidates’ heated exchange a few minutes later was accompanied by one-word reactions — “wow” chief among them.

The social network was a virtual spin room, one used especially aggressively by surrogates for Mr. Obama to assert that he had improved since the debate two weeks ago, when his performance was widely derided.

A few minutes into the debate Stephanie Cutter, the Obama deputy campaign manager, reposted a comment from a supporter who said, “Welcome back, Mr. President.” Then she reposted another: “Obama is back.”

Commentators who had criticized Mr. Obama two weeks ago — most notably Andrew Sullivan of The Daily Beast — seemed to agree.

“Obama’s back on,” Mr. Sullivan wrote on his live blog at 9:07 p.m. “I recognize this guy. Energy; focus; ability to relate.”

Obama campaign aides also promoted a hashtag with the phrase #RealRomney, pushing the point of view that Mr. Romney’s real opinions are unknowable — foreshadowing Mr. Obama’s claims that Mr. Romney’s answers on Tuesday night were not accurate.

Fact-Check: Candidates on Coal

President Obama said that coal jobs and coal production was up. True, but the increases are modest.Read More

Mr. Romney said that Mr. Obama was hostile to coal and that the administrator of the Environmental Protection Agency had said that no future coal-burning plants would be built in the United States. In fact, the administrator, Lisa P. Jackson, proposed emissions standards for future coal-burning plants that would require them to be as clean as a plant using natural gas as a fuel. The technology to accomplish this does not yet exist, but utilities are swiftly shifting from coal to natural gas anyway because natural gas is now so plentiful and cheap.

Mr. Obama said that coal jobs and coal production were up during his administration, which is true, but the increases are modest and much of the additional coal production is being shipped overseas.

Mr. Obama also noted that as governor of Massachusetts Mr. Romney had cracked down on one coal-burning plant, saying that coal “kills people.” Mr. Romney did in fact accuse a utility of failing to live up to its promises to clean up emissions from one Massachusetts coal plant, saying, “I will not create jobs or hold jobs that kill people. And that plant kills people and PG&E has been given a notice to have it cleaned up by 2004 and they have thumbed their nose at the people of Massachusetts and Salem Harbor by not cleaning it up on time. “

Mitt Romney’s campaign, in an effort to appeal to women who hold more moderate views on reproductive issues, is releasing a new commercial that highlights his support for contraception and abortion in limited circumstances.

“You know, those ads say Mitt Romney would ban all abortions and contraception seemed a bit extreme, so I looked into it,” says a woman identified as Sarah Minto, who is shown on camera searching on Google for “Romney on abortion.”

Ms. Minto adds: “It turns out Romney doesn’t oppose contraception at all. In fact, he thinks abortion should be an option in cases of rape, incest or to save a mother’s life.”

The ad is Mr. Romney’s most aggressive attempt to rebut attempts by the Obama campaign to paint him as extreme on women’s rights. Read more…

Fact-Check: Spending, Borrowing and Higher Taxes?

Mr. Romney just charged that “a recent study has shown that people in the middle class will see $4,000 a year higher taxes as a result of the spending and borrowing of this administration” — a claim that FactCheck.org recently examined and labeled “nonsense.”

Mr. Romney repeated his assertion that all the increase in domestic oil and gas production had come on private, not public lands, and that the Obama administration had cut the number of oil and gas drilling permits on public lands in half. Neither assertion is fully true.Read More

Mr. Romney and Mr. Obama engaged in a sharp exchange on energy policy, sparked by a question on gasoline prices that never got answered. They disagreed about oil production on public as well as private lands, a dispute they have had throughout the campaign.

Oil and gas production on public lands has fluctuated during the Obama administration, but it has increased modestly (about 13 percent for oil and about 6 percent for gas) in the first three years of the Obama presidency, compared to the last three years of the Bush administration, according to an analysis from the Energy Information Administration. Production on private lands has increased more quickly, particularly through hydraulic fracturing for oil and gas in Texas, North Dakota and the Marcellus Shale formation in Pennsylvania and Ohio.

Regarding drilling permits, the Department of Interior produced a report earlier this year showing that drilling permits received and issued by the agency had indeed declined from the last years of the Bush administration to the first years of the Obama administration. In fiscal year 2007, the government issued 8,964 permits to drill on public lands; in 2008 the figure was 7,846. The numbers for 2009 and 2010 were 5,306 and 5,237. This is a reduction, but not by half, as Mr. Romney asserted.

Mr. Obama said here that 7,000 permits had been granted but were not being used by oil companies, an accurate figure, according to the Interior Department.

The administration froze all deep-water drilling and slowed shallow-water drilling in the Gulf of Mexico after the Deepwater Horizon blowout and spill in 2010. Since then, the Interior Department has approved more than 750 drilling permits for the gulf and production is approaching pre-spill levels, although it is below what was projected before the accident.

Before Deepwater Horizon, gulf oil production was 1.75 million barrels a day, and it was projected to increase to 2.2 million barrels a day by this year.

Instead, because of the yearlong halt on new drilling, production is about 700,000 barrels a day lower than forecast. Much of that oil is being replaced by Saudi imports, experts said.

Mr. Obama stated that renewable energy production had doubled during his presidency, which is true, and that oil imports were at their lowest level in 16 years, also accurate. He also said that the boom in natural gas production could produce 600,000 new jobs, a highly optimistic estimate, but he qualified it with the word “potentially.”

But Mr. Obama mischaracterized Mr. Romney’s energy plan, saying it was written by oil companies and favored only traditional sources of energy — oil, gas and coal. But Mr. Romney’s energy plan does include a place for renewables, although he would sharply cut back on federal subsidies for wind, solar and other alternative energy sources.

Mr. Romney, to illustrate his charge that Mr. Obama was hostile to the oil industry, said that the Obama administration had criminally prosecuted oil companies working in North Dakota for killing migratory birds. True. In September 2011, the United States attorney for North Dakota charged seven oil and natural gas companies for killing 28 migratory birds found dead near oil waste lagoons.

Fact-Check: Balancing the Budget

Mr. Romney correctly stated that he produced a balanced budget during each of his four years in office. But that’s hardly unusual: every governor does it. The Massachusetts constitution requires that the budget be balanced.

Fact-Check: No Tax Increases?

Can Mr. Romney keep his promise not to increase taxes on working-class families? Studies show that is a promise that might be hard for him to keep.Read More

“I will not under any circumstances increase taxes on the middle class,” Mr. Romney promised at the debate, taking aim at Democratic arguments that he would raise taxes on working-class families to finance tax cuts for the rich.

But studies show that is a promise that might be hard for Mr. Romney to keep. Mr. Romney has said he wants to get rid of the alternative minimum tax and cut marginal tax rates by 20 percent, without widening the deficit. He would accomplish that goal by clearing out the underbrush of credits, loopholes and preferences in the code, though not those for investment and savings. He has also promised that his plan will be “distributionally neutral” – that he will not raise the tax burden on the poor or middle class.

But, according to a study by the respected Tax Policy Center, if you cut tax rates by 20 percent, you give the wealthy a multibillion-dollar tax break. Even if you take away all of their credits and loopholes and preferential rates, the gap is still about $86 billion in 2015. If the rich are paying less, then the poor and middle class must pay more if you’re going to raise the same amount of money.

In the debate, Mr. Romney said that he might put a cap on deductions — $25,000 per household, he suggested — to raise money to pay for the rate cuts. But tax economists said such a proposal still might not raise enough money from the wealthy and might result in an increased tax burden on the middle class or a bigger deficit.

Fact-Check: College Graduates Without Jobs?

Mr. Romney said that “with half of college kids graduating this year without a college — or excuse me, without a job and without a college-level job, that’s just unacceptable.” Is it true that half the students graduating from college this year don’t have a “college-level job”?

It’s not clear what numbers he is referring to, but Mr. Romney might be talking about numbers from last year. An analysis of 2011 Labor Department data by researchers at Northeastern University, Drexel University, and the Economic Policy Institute, a liberal think tank, found that about 1.5 million, or 53.6 percent, of people with bachelor’s degrees under the age of 25 last year were jobless or employed in jobs that did not require a college degree. That was the highest share in at least 11 years.

Fact-Check: Tax Increase on Small Business

Mr. Romney just warned that Mr. Obama’s plan to let the Bush-era income tax cuts for the highest-earning Americans expire would hurt small businesses. But 97 percent of small businesses do not earn enough to be hit by the higher rates.Read More

Mr. Romney just warned, as he often does, that Mr. Obama’s plan to let the Bush-era income tax cuts for the highest-earning Americans expire would hurt small businesses. But 97 percent of small businesses do not earn enough to be hit by the higher rates, according to the Joint Committee on Taxation of Congress.

Mr. Obama wants to roll back the Bush tax cuts on income above $200,000 for individuals and income above $250,000 for households, raising the top marginal rate to 39.6 percent from 35 percent now. Some small businesses, who file taxes as “S corporations,” would be hit by the higher rates, but the Joint Committee on Taxation estimates that only 3 percent would earn enough to be hit by the new, higher top marginal rates. And not all of those businesses are exactly small: thousands of them would have receipts of more than $50 million a year, the committee found.

The Romney campaign noted that those few businesses play an important role and said that they should not be burdened with higher taxes.

Of the businesses that would be subjected to the higher rates, many are sole proprietors — a classification so amorphous it can include everyone from corporate executives who earn income on rental property to entertainers, hedge fund managers and investment bankers.

Pluralities of likely voters and independent voters have said in recent polls that they supported letting the Bush-era tax cuts on higher earners expire.

Would repealing those tax cuts kill jobs? Economists generally agree that raising taxes, and taking money that would otherwise cycle through the economy, can cost jobs; that is one of the reasons Mr. Obama’s stimulus plan included tax cuts. But it is worth noting that the rates Mr. Obama wants to return to were last seen during the Clinton administration — a time when the nation created 22.7 million jobs, as the Romney campaign itself has noted.

Brian Blanco for The New York TimesAlyse Siegrist took notes as she watched the second presidential debate between President Obama and Mitt Romney at a debate-watching party in Largo, Fla.

LARGO, Fla. – Mr. Obama’s first aggressive-looking jabs at Mr. Romney, on the issue of oil and gas, drew some praise. “Throw it back at him, baby!” Mr. Bach said.

When the candidates stepped toward each other and traded questions directly, Mr. Fechko wondered when the moderator would step in. “The aggression is making Romney look rude, to me. He’s speaking and I didn’t notice Candy Crowley recognize him.”

Fact-Check: 'Let Detroit Go Bankrupt'?

Did Mitt Romney really say “Let Detroit Go Bankrupt”? Yes. Though he did not write the headline that continues to haunt him — that task fell to an editor – he did argue in a New York Times op-ed article that General Motors and Chrysler should go through a managed bankruptcy. Read More

But while those companies did ultimately file for bankruptcy, Mr. Romney’s claim ignores key facts about the automaker’s stability at the time.

Detroit was so fragile at the time that without the government assistance it received before heading into a court-supervised bankruptcy process, it could have collapsed.

At the time Mr. Romney wrote that article (he did not write the headline himself, but had to approve it per a New York Times policy allowing outside op-ed writers the chance to veto any editors’ changes), the financial markets had ground to a halt. It was November 2008, and there was little available liquidity for anyone seeking financing. There were certainly no financial institutions — not even Bain Capital, Mr. Romney’s private equity firm — looking to invest to the tune of the $80 billion the car companies needed at the time.

No private companies would come to the industry’s aid, and the only path through bankruptcy would have been Chapter 7 liquidation, not the more orderly Chapter 11 reorganization that the company ultimately followed, people inside and outside the car companies have said.

In fact, the task force asked Bain if it was interested in investing in General Motors’ European operations, according to one person with direct knowledge of the discussions.

Here’s another bit of conventional wisdom that we can throw out the window: That candidates would be restrained from attacking each other, directly and intensely, because there is an audience in the room. Already, Mr. Obama and Mr. Romney are facing each other, challenging each other and acting as if there is not another person in the room. “You’ll get your chance in a moment,” Mr. Romney said.

Fact-Check: Pell Grants for College

Mr. Romney said he wanted to keep the Pell Grant program growing. This a new position for him Read More

Barely a minute into his first reply of the debate, Mr. Romney said, “I want to make sure we keep our Pell Grant program growing” a new position for him. In the first debate, he said, “I don’t have any plan to cut education funding and grants that go to people going to college,” and even that position came as a surprise to many analysts.

The governor and his campaign have repeatedly criticized President Obama’s expansion of the Pell Grant program, which they have said is unsustainable. Mr. Romney’s position paper on education says he would “refocus Pell Grants dollars on the students who need them most.” For months, this was widely interpreted as meaning that fewer people would qualify for Pell Grants — a question the Romney campaign declined to clarify.

Mr. Romney would also restore banks to their role in making student loans. Mr. Obama eliminated that role and used some of the savings to pay for the Pell Grant expansion.

It took less than a minute for Mr. Obama to take a swing at his rival, accusing Mr. Romney of saying that he wanted Detroit to go bankrupt four years ago.

“When Governor Romney said we should let Detroit go bankrupt, I bet on the American auto industry,” Mr. Obama said.

That dig produced exactly the expected response from Mr. Romney, who indignantly charged that the president eventually pushed to take the auto companies through bankruptcy too.

“That was precisely what I recommended and what happened,” Mr. Romney said.

But the president fired right back, quickly becoming aggressive the way his supporters said he did not during the first debate.He accused Mr. Romney of supporting a bankruptcy for the auto industry without supporting the financial resources that made it possible. And he quickly attacked Mr. Romney as an elitist who cares about the rich.

“Governor Romney doesn’t have a five-point plan. He has a one-point plan,” Mr. Obama said. “And that is to make sure folks at the top play by a different set of rules.”

LARGO, Fla. – The first few moments of the debate brought an observation: “So Romney has a blue tie on but the President is wearing red?” Mr. Fechko said, sounding a bit amused. “I just find it odd. But it probably has no real meaning. It’s nothing official, but we associate red with Republicans and blue with Democrats. They don’t do anything without calculation, so perhaps it does mean something.”

Fact-Check: 12 Million Jobs

Mr. Romney has promised to create 12 million jobs over the next four years if he is elected president. That is actually about as many jobs as the economy is already expected to create, according to some economic forecasters.Read More

In its semiannual long-term economic forecast released in April, Macroeconomic Advisers projected that the economy would add 11.8 million jobs from 2012 to 2016. Moody’s Analytics, another forecasting firm, projects similar job growth. That means Mr. Romney believes his newly announced policies would add an extra 200,000 jobs on top of what people already expected, or a jobs bonus of about 2 percent.

Mark Zandi, the chief economist at Moody’s Analytics, said that he expected the economy to remain on about the same path regardless of who is elected, under the assumption that whoever wins will “reasonably gracefully address the fiscal cliff, increase the Treasury debt ceiling without major incident, and achieve something close to fiscal sustainability.”

Mr. Romney’s camp may be suggesting that his policies would create 12 million jobs in excess of those already on track to be produced.

When asked by The Washington Post how the 12 million number was produced, the campaign cited three studies, all of which were problematic in this context.

One study finding that seven million jobs would be created by Mr. Romney’s tax plan refers to job creation over a decade, not four years.

Another apparently intended to support the claim that Mr. Romney’s energy policies would create three million jobs, but that number referred to an eight-year projection for policies largely already in place, not a four-year time frame for an alternative policy proposed by Mr. Romney.

Finally, Mr. Romney and his campaign have said that two million jobs could be created if the United States got tougher on China’s infringement of intellectual property rights. That number has been sourced to a May 2011 report from the International Trade Commission.

It did not specifically analyze a Romney proposal; it simulated what would happen if China enacted a “substantial improvement” in intellectual property rights so that intellectual property was about as protected in China as it is in the United States. It found that the United States would gain about 2.1 million full-time equivalent jobs, at least under the economic conditions the country faced in 2011. It is not clear how the United States could force China to effect this change, though.

Brian Blanco for The New York TimesChuck Fechko, left, looks on as Ernie Bach, state chairman of the Independent Party of Florida, gathered his television remotes to record Fox News before the start of the second presidential debate.

LARGO, Fla. – Here on the shores of the Gulf of Mexico, in a swing county in an important swing state, the leader of the local Independent Party has gathered several friends to debate the debate — coffee, red sangria and beers in hand.

“Well, we’ll see how many distortions come out tonight,” said Ernie Bach, the Independent Party’s state chairman and a longtime political activist. “Perception is reality. Say something over and again, and people will believe it.”

Mr. Nystrom’s not entirely unserious idea of the moment is to start his own “super PAC” to counter the weight of the Democratic and Republican fund-raisers who have, in his words, “so distorted this race.”

For now, with the naming issue on the back burner, attention has turned to what people want to see Tuesday night, in what they expect will be yet another crucial night for both President Obama and his Republican challenger, Mitt Romney.

“This one should be pretty good, given what’s already happened,” Mr. Fechko said. “Common wisdom in the past has been that debates are entertaining and interesting. But these seem to actually change poll numbers. So anything is possible.”

Doug Mills/The New York TimesJohn H. Sununu, a former Republican governor of New Hampshire, joked with a number of Romney advisers in the spin room prior to the second presidential debate at Hofstra University.

Pencils sharpened?

Fresh batteries in voice recorders?

O.K., let’s go. It’s time to pre-spin the debate. And here they come, into the blue-carpeted pit at the front of the press center, a thundering herd of Republican and Democratic surrogates to foreshadow themes and amplify their candidates’ messages.

(Reader warning: some mature content to follow)

Gov. Bob McDonnell, Republican of Virginia, asked how Mr. Romney would parry President Obama’s effort to paint him as unfriendly to women: “The whole theory that Republicans are somehow engaged in a war on women is very much contrived. Everybody knows that. The recent polls show women have actually given Mitt Romney his bump.’’

Senator John Kerry, Democrat of Massachusetts (and stand-in for Mr. Romney in the president’s debate prep), on how Mr. Romney would portray himself: “Tonight I’ll bet you’ll hear him stand up there and say, ‘Wow, was I bipartisan in Massachusetts, I want to do for the country what I did in Massachusetts.’ Well, country, be warned. What he did in Massachusetts according to the speaker was give marching orders. According to the Senate president, was be disengaged.’’

John H. Sununu, a former Republican governor of New Hampshire, asked what he thought of Secretary of State Hillary Rodham Clinton’s accepting responsibility for American deaths in Benghazi, Libya: “She deserves credit for trying to save the president’s butt and throwing herself under the bus. But shame on the president for having her do that.’’

Alan Simpson, the former Wyoming Senator, on why Representative Paul D. Ryan rejected the bipartisan report of the Simpson-Bowles debt reduction commission: “I said, ‘If you voted against it because you’re afraid of Grover Norquist, I have no respect for you whatsoever.’ He said, ‘No, we feel if you get rid of the employer deduction of employee health care, the employers will panic and go to Obamacare’. I said, ‘That’s good enough for me.’ “

Hey, this guy’s pretty good. Let’s ask another question: Is Mr. Romney being honest with voters about how he will pay for his tax cuts?

“Nobody’s honest with anybody. It’s mush all around. They haven’t mentioned Social Security solvency once. These kids” – indicating Hofstra University students looking on – “will be picking crap with the chickens when they’re 65.”

What are Mr. Obama’s top advisers telling him ahead of Tuesday night’s debate?

For the most part, that’s a secret. But a memo from Ron Klain, the president’s chief debate coach, may give some clues.

The memo of debate-prep “rules,” penned years ago and posted online again recently by Third Way, a Democratic-leaning think tank in Washington, urges candidates to write their “dream post-debate headline” as they prepare.

“As you consider potential answers, or lines, or any other element of debate strategy and tactics, ask yourself: Is this approach helping to win that “dream” headline?” Mr. Klain writes.

Mr. Obama got none of his dream headlines after the first debate. Nor did he satisfy Mr. Klain’s second rule in the seven-page memo: to develop a list of “three items you MUST say in the debate.”

The president was roundly criticized after the first debate for failing to mention any of his top priorities: Mr. Romney’s “47 percent” comment; the abortion issue; Bain Capital; or Mr. Romney’s taxes. It’s possible Mr. Klain has stressed rule No. 2 in the days leading up to this debate.

And then there’s rule No.10, which gets at one of the other criticisms of Mr. Obama’s initial performance — that he was sleepwalking through the first debate. “Punches are good, counterpunches are better,” says rule No. 10.

“If you develop five zippy replies to your opponents’ five most commonly used lines, the odds are high that you will get a chance to use two or three,” Mr. Klain writes. “And remember to also game out your opponents’ likely replies to your most common lines: nothing is more effective in a debate than a counter-counter punch!”

Among some of the more interesting ones: Rule 3 encourages candidates to study what their opponent has been saying in the days just before the debate. “All candidates are creatures of habit. You can use that to your advantage: 90% of what your opponent will say in the debate will have come out of his mouth in the week before the debate,” Mr. Klain writes.

Or Rule 13, which says that a candidate can lose a debate at any time during the event, but that “you can only win it in the first 30 minutes.” He explains: “The viewers, the reporters and even your opponent form a sense of the debate dynamic in the early going. Indeed, for debates held at night, reporters (on deadline) usually write first drafts of their stories before the debate is half over.”

And, finally, Rule 20: “If in doubt, don’t.” Candidates are often uncertain if something they say will come out right, Mr. Klain writes.

“At that moment remember the advice that some elementary school teacher once gave you: ‘If in doubt, don’t,’ ” Mr. Klain writes. “Better to fail to make a point during a debate (leaving open the possibility it can be made post-debate) than to make a point that goes awry.”

Mitt Romney may have a unseen weapon for this town hall-style debate: dozens of secretive practice sessions that began many months ago.

Aides to Mr. Romney began organizing frequent, off-the-record discussions with voters six months ago, with a specific goal in mind: making the candidate comfortable talking to ordinary people about their troubles and supplying him with anecdotes to tell during crucial moments of the campaign.

The sessions, typically held before or after public events in far-flung locales, around a small table with light food and beverages, had the advantage of being shielded from reporters, so that any of Mr. Romney’s awkward moments or offhand remarks remained private. Aides said he had witnessed — and learned to react to — men and women become emotional about everything from foreclosed homes to their children’s academic achievements.

Most important, the roundtable discussions offered Mr. Romney a chance to become a practiced retail politician in intimate settings, something at which he is likely to excel Tuesday night at Hofstra.

President Obama’s campaign has sent dozens of fund-raising e-mails to supporters from Michelle Obama, the first lady.

But the one that arrived in in boxes at just before 8 o’clock tonight uses a word that none of them did before in describing her husband.

“Fighting.”

In the fund-raising pitch, Mrs. Obama describes herself as proud of her husband and eager to see him on the stage facing Mr. Romney for a second time. And she obliquely acknowledges the criticism that Mr. Obama did not seem to be aggressive the last time.

“Tonight at the debate, you’re going to see the guy who will always be out there fighting tirelessly for you,” she writes. “Show Barack you’re with him by donating $5 or more.”

What happens when you are quoted saying something unflattering about the president just days before a critical second debate?

Well, if you’re the leader of a Democratic-leaning think tank in Washington and one of the president’s most visible supporters, you apologize, fast.

That’s what happened to Neera Tanden, the president of the Center for American Progress.

Ms. Tanden was quoted in a New York Magazine article this week as saying the following about Mr. Obama: “The truth is, Obama doesn’t call anyone, and he’s not close to almost anyone. It’s stunning that he’s in politics, because he really doesn’t like people. My analogy is that it’s like becoming Bill Gates without liking computers.”

That’s pretty tough stuff, especially coming from the leader of an organization dedicated to implementing policies that Mr. Obama supports. (Ms. Tanden was a top supporter of Hillary Clinton during the 2008 Democratic primaries.)

It’s a sure bet that folks at the White House, and in Mr. Obama’s Chicago headquarters, were not happy at all.

Eric Gay/Associated PressSupporters cheered for President Obama on the campus of Hofstra University before the start of the second presidential debate on Tuesday in Hempstead, N.Y.

HEMPSTEAD, N.Y. – Two hours before the candidates step on the stage at Hofstra University here, the cavernous spin room is already crackling with narratives and counternarratives – most about how pugilistic President Obama is likely to be.

“They all say he’s going to come out swinging,” said Senator Rob Portman, the Ohio Republican who played Mr. Obama in mock debates to prepare Mitt Romney. “He’s going to be a new Barack Obama – new, different, improved.”

But an hour earlier, Stephanie Cutter, Mr. Obama’s deputy campaign manager, insisted, “He is not looking to come here to score punches on Mitt Romney; he’s coming in here to describe what a second term of an Obama presidency would look like.”

She said the expectations of a very combative Mr. Obama were largely a creation of the Romney campaign. At the same time, Ms. Cutter said the president would be “passionate” about making his case for a second term. She said that Mr. Obama would hold Mr. Romney to account for his statements, but that it would not be his primary thrust.

“We’ll do our best to keep Mitt Romney honest,” she said, “but that could take all night.” Read more…

If either President Obama or Mitt Romney had a robotic sidekick like the one in the campy, 1960s television show “Lost in Space,” it might now be bleeping wildly and warning: “Danger! Danger!”

The threat? Voters.

Both candidates have had some of their most awkward and politically fraught moments when confronted directly by voters.

Mr. Obama was caught off guard during a 2010 economic town hall forum on CNBC when an African-American woman declared herself profoundly disappointed in him. He grinned awkwardly and then rambled for four minutes, providing new evidence of the political peril from a still sluggish economy.

At the Iowa State Fair in 2011, Mr. Romney’s answer to a combative voter provided one of the most enduring — and damaging — moments in his campaign. “Corporations are people, too, my friend,” a defensive Mr. Romney responded, a line that would dog him in the months ahead.

Tonight, there will many opportunities for such a moment, as described in the following piece. Read more …

— Michael D. Shear

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